Coverage for pySDC/projects/FastWaveSlowWave/AcousticAdvection_1D_FD_imex_multiscale.py: 100%

1import numpy as np 

2 

3from pySDC.implementations.problem_classes.AcousticAdvection_1D_FD_imex import acoustic_1d_imex 

4 

5 

6# noinspection PyUnusedLocal 

7class acoustic_1d_imex_multiscale(acoustic_1d_imex): 

8 """ 

9 Example implementing the one-dimensional IMEX acoustic-advection with multiscale initial values 

10 """ 

11 

12 def u_exact(self, t): 

13 """ 

14 Routine to compute the exact solution at time t 

15 

16 Args: 

17 t (float): current time 

18 

19 Returns: 

20 dtype_u: exact solution 

21 """ 

22 

23 sigma_0 = 0.1 

24 k = 7.0 * 2.0 * np.pi 

25 x_0 = 0.75 

26 x_1 = 0.25 

27 

28 ms = 1.0 

29 

30 me = self.dtype_u(self.init) 

31 me[0, :] = np.exp(-np.square(self.mesh - x_0 - self.cs * t) / (sigma_0 * sigma_0)) + ms * np.exp( 

32 -np.square(self.mesh - x_1 - self.cs * t) / (sigma_0 * sigma_0) 

33 ) * np.cos(k * (self.mesh - self.cs * t) / sigma_0) 

34 me[1, :] = me[0, :] 

35 

36 return me